Question

O jaki wektor należy przesunąć wykres funkcji f(x)=3,aby otrzymać wykres funkcji g?
a)
b)
c)
d)

Answer 1

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f(x) = ax²
g(x) = ax² + bx + c
g(x) =a(x-p)² + q
p = -b/2a
q = g(x=p)= a(p-p)² + q = q
q = g(p) =ap² + bp + c
→
n =  [p; q]
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a)
p =-b/2a =-6/(2*3) = -1
q = f(-1) =3*1² - 6*1 + 5 = 2
→
n = [-1; 2]
b)
p =-b/2a = 6/(2*3) = 1
q = f(1) =3*1² - 6*1 + 5 = 2
→
n = [1; 2]
c)
p =-b/2a = -3/(2*3) =  - 0,5
q = f(- 0,5) =3*(- 0,5)²+3*(- 0,5)+1 = 0,25
→
n = [- 0,5; 0,25]
d)
p =-b/2a = -12/(2*3) = -2
q = f(-2) = 3(-2)²+12*(-2)+12 = 0
→
n = [- 2;  0]